The inverse problem of reconstructing the timewise term along with the temperature in the nonlocal diffusion equation with initial and boundary conditions and additional measurement (an integral and partial heat flux) is, for the first time, numerically investigated. This inverse problem appears extensively in the modeling of various phenomena in engineering and physics. The inverse problem considered in this paper has a unique solution. A Crank–Nicolson FDM is applied as a direct solver. The resulting nonlinear problem is solved using the MATLAB subroutine to minimize the objective functional. The Tikhonov regularization method is applied where necessary. A pair of examples, with smooth and non-smooth continuous timewise term, are discussed to assess the accuracy and stability of the numerical solutions.

首次在数值上研究了用初始和边界条件以及附加测量（积分和部分热通量）在非局部扩散方程中重建时间项和温度的反问题。这个逆问题广泛出现在工程和物理学中各种现象的建模中。本文考虑的反问题具有独特的解决方案。Crank–Nicolson FDM被用作直接求解器。由此产生的非线性问题使用MATLAB子例程来解决，以最小化目标函数。必要时应用Tikhonov正则化方法。讨论了具有平滑和非平滑连续时间项的一对示例，以评估数值解的准确性和稳定性。